# The p-Value in One-Sample Tests for the Mean

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In reporting the result of a significance test, showing the observed test statistic and its location in the null distribution along with the tail area is a helpful and frequently used graphic. This Demonstration makes it easy to construct this plot for the one-sample test for the population mean of a normal distribution. The effect of sample size, the assumption that the population variance is known or not, as well the question of using a one-sided or two-sided test may also be explored.

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Contributed by: Ian McLeod (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: versus , assumed known and based on a sample of 10 observations, so

Snapshot 2: as in Snapshot 1, but unknown and , yielding

Snapshot 3: and , and , yielding . A two-sided test is used.

Snapshot 4: As in Snapshot 3, but suppose is based on

Snapshot 5: with known variance

The two-sided test is always more conservative and for this reason many researchers discourage the use of one-sided tests [1].

[1] G. van Belle, *Statistical Rules of Thumb, *2nd ed., New York: Wiley, 2008 p. 16.

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